{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#| default_exp models.nhits"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#| hide\n",
    "%load_ext autoreload\n",
    "%autoreload 2"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# NHITS"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Long-horizon forecasting is challenging because of the *volatility* of the predictions and the *computational complexity*. To solve this problem we created the Neural Hierarchical Interpolation for Time Series (NHITS). `NHITS` builds upon `NBEATS` and specializes its partial outputs in the different frequencies of the time series through hierarchical interpolation and multi-rate input\n",
    "processing. On the long-horizon forecasting task `NHITS` improved accuracy by 25% on AAAI's best paper award the `Informer`, while being 50x faster.\n",
    "\n",
    "The model is composed of several MLPs with ReLU non-linearities. Blocks are connected via doubly residual stacking principle with the backcast $\\mathbf{\\tilde{y}}_{t-L:t,l}$ and forecast $\\mathbf{\\hat{y}}_{t+1:t+H,l}$ outputs of the l-th block. Multi-rate input pooling, hierarchical interpolation and backcast residual connections together induce the specialization of the additive predictions in different signal bands, reducing memory footprint and computational time, thus improving the architecture parsimony and accuracy.\n",
    "\n",
    "**References**<br>\n",
    "-[Boris N. Oreshkin, Dmitri Carpov, Nicolas Chapados, Yoshua Bengio (2019). \"N-BEATS: Neural basis expansion analysis for interpretable time series forecasting\".](https://arxiv.org/abs/1905.10437)<br>\n",
    "-[Cristian Challu, Kin G. Olivares, Boris N. Oreshkin, Federico Garza, Max Mergenthaler-Canseco, Artur Dubrawski (2023). \"NHITS: Neural Hierarchical Interpolation for Time Series Forecasting\". Accepted at the Thirty-Seventh AAAI Conference on Artificial Intelligence.](https://arxiv.org/abs/2201.12886)<br>\n",
    "-[Zhou, H.; Zhang, S.; Peng, J.; Zhang, S.; Li, J.; Xiong, H.; and Zhang, W. (2020). \"Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting\". Association for the Advancement of Artificial Intelligence Conference 2021 (AAAI 2021).](https://arxiv.org/abs/2012.07436)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![Figure 1. Neural Hierarchical Interpolation for Time Series (NHITS).](imgs_models/nhits.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#| export\n",
    "from typing import Tuple, Optional\n",
    "\n",
    "import numpy as np\n",
    "import torch\n",
    "import torch.nn as nn\n",
    "import torch.nn.functional as F\n",
    "\n",
    "from neuralforecast.losses.pytorch import MAE\n",
    "from neuralforecast.common._base_windows import BaseWindows"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#| hide\n",
    "import logging\n",
    "import warnings\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "from fastcore.test import test_eq\n",
    "from nbdev.showdoc import show_doc\n",
    "from neuralforecast.utils import generate_series"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#| hide\n",
    "logging.getLogger(\"pytorch_lightning\").setLevel(logging.ERROR)\n",
    "warnings.filterwarnings(\"ignore\")\n",
    "\n",
    "#plt.rcParams[\"axes.grid\"]=True\n",
    "plt.rcParams['font.family'] = 'serif'\n",
    "#plt.rcParams[\"figure.figsize\"] = (4,2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#| export\n",
    "class _IdentityBasis(nn.Module):\n",
    "    def __init__(self, backcast_size: int, forecast_size: int, \n",
    "                 interpolation_mode: str, out_features: int=1):\n",
    "        super().__init__()\n",
    "        assert (interpolation_mode in ['linear','nearest']) or ('cubic' in interpolation_mode)\n",
    "        self.forecast_size = forecast_size\n",
    "        self.backcast_size = backcast_size\n",
    "        self.interpolation_mode = interpolation_mode\n",
    "        self.out_features = out_features\n",
    " \n",
    "    def forward(self, theta: torch.Tensor) -> Tuple[torch.Tensor, torch.Tensor]:\n",
    "\n",
    "        backcast = theta[:, :self.backcast_size]\n",
    "        knots = theta[:, self.backcast_size:]\n",
    "\n",
    "        # Interpolation is performed on default dim=-1 := H\n",
    "        knots = knots.reshape(len(knots), self.out_features, -1)\n",
    "        if self.interpolation_mode in ['nearest', 'linear']:\n",
    "            #knots = knots[:,None,:]\n",
    "            forecast = F.interpolate(knots, size=self.forecast_size, mode=self.interpolation_mode)\n",
    "            #forecast = forecast[:,0,:]\n",
    "        elif 'cubic' in self.interpolation_mode:\n",
    "            if self.out_features>1:\n",
    "                raise Exception('Cubic interpolation not available with multiple outputs.')\n",
    "            batch_size = len(backcast)\n",
    "            knots = knots[:,None,:,:]\n",
    "            forecast = torch.zeros((len(knots), self.forecast_size), device=knots.device)\n",
    "            n_batches = int(np.ceil(len(knots)/batch_size))\n",
    "            for i in range(n_batches):\n",
    "                forecast_i = F.interpolate(knots[i*batch_size:(i+1)*batch_size], \n",
    "                                           size=self.forecast_size, mode='bicubic')\n",
    "                forecast[i*batch_size:(i+1)*batch_size] += forecast_i[:,0,0,:] # [B,None,H,H] -> [B,H]\n",
    "            forecast = forecast[:,None,:] # [B,H] -> [B,None,H]\n",
    "\n",
    "        # [B,Q,H] -> [B,H,Q]\n",
    "        forecast = forecast.permute(0, 2, 1)\n",
    "        return backcast, forecast"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#| exporti\n",
    "ACTIVATIONS = ['ReLU',\n",
    "               'Softplus',\n",
    "               'Tanh',\n",
    "               'SELU',\n",
    "               'LeakyReLU',\n",
    "               'PReLU',\n",
    "               'Sigmoid']\n",
    "\n",
    "POOLING = ['MaxPool1d',\n",
    "           'AvgPool1d']\n",
    "\n",
    "class NHITSBlock(nn.Module):\n",
    "    \"\"\"\n",
    "    NHITS block which takes a basis function as an argument.\n",
    "    \"\"\"\n",
    "    def __init__(self, \n",
    "                 input_size: int,\n",
    "                 h: int,\n",
    "                 n_theta: int,\n",
    "                 mlp_units: list,\n",
    "                 basis: nn.Module,\n",
    "                 futr_input_size: int,\n",
    "                 hist_input_size: int,\n",
    "                 stat_input_size: int,\n",
    "                 n_pool_kernel_size: int,\n",
    "                 pooling_mode: str,\n",
    "                 dropout_prob: float,\n",
    "                 activation: str):\n",
    "        super().__init__()\n",
    "\n",
    "        pooled_hist_size = int(np.ceil(input_size/n_pool_kernel_size))\n",
    "        pooled_futr_size = int(np.ceil((input_size+h)/n_pool_kernel_size))\n",
    "\n",
    "        input_size = pooled_hist_size + \\\n",
    "                     hist_input_size * pooled_hist_size + \\\n",
    "                     futr_input_size * pooled_futr_size + stat_input_size\n",
    "\n",
    "        self.dropout_prob = dropout_prob\n",
    "        self.futr_input_size = futr_input_size\n",
    "        self.hist_input_size = hist_input_size\n",
    "        self.stat_input_size = stat_input_size\n",
    "        \n",
    "        assert activation in ACTIVATIONS, f'{activation} is not in {ACTIVATIONS}'\n",
    "        assert pooling_mode in POOLING, f'{pooling_mode} is not in {POOLING}'\n",
    "\n",
    "        activ = getattr(nn, activation)()\n",
    "\n",
    "        self.pooling_layer = getattr(nn, pooling_mode)(kernel_size=n_pool_kernel_size,\n",
    "                                                       stride=n_pool_kernel_size, ceil_mode=True)\n",
    "\n",
    "        # Block MLPs\n",
    "        hidden_layers = [nn.Linear(in_features=input_size, \n",
    "                                   out_features=mlp_units[0][0])]\n",
    "        for layer in mlp_units:\n",
    "            hidden_layers.append(nn.Linear(in_features=layer[0], \n",
    "                                           out_features=layer[1]))\n",
    "            hidden_layers.append(activ)\n",
    "\n",
    "            if self.dropout_prob>0:\n",
    "                #raise NotImplementedError('dropout')\n",
    "                hidden_layers.append(nn.Dropout(p=self.dropout_prob))\n",
    "\n",
    "        output_layer = [nn.Linear(in_features=mlp_units[-1][1], out_features=n_theta)]\n",
    "        layers = hidden_layers + output_layer\n",
    "        self.layers = nn.Sequential(*layers)\n",
    "        self.basis = basis\n",
    "\n",
    "    def forward(self, insample_y: torch.Tensor, futr_exog: torch.Tensor,\n",
    "                hist_exog: torch.Tensor, stat_exog: torch.Tensor) -> Tuple[torch.Tensor, torch.Tensor]:\n",
    "\n",
    "        # Pooling\n",
    "        # Pool1d needs 3D input, (B,C,L), adding C dimension\n",
    "        insample_y = insample_y.unsqueeze(1)\n",
    "        insample_y = self.pooling_layer(insample_y)\n",
    "        insample_y = insample_y.squeeze(1)\n",
    "\n",
    "        # Flatten MLP inputs [B, L+H, C] -> [B, (L+H)*C]\n",
    "        # Contatenate [ Y_t, | X_{t-L},..., X_{t} | F_{t-L},..., F_{t+H} | S ]\n",
    "        batch_size = len(insample_y)\n",
    "        if self.hist_input_size > 0:\n",
    "            hist_exog = hist_exog.permute(0,2,1) # [B, L, C] -> [B, C, L]\n",
    "            hist_exog = self.pooling_layer(hist_exog)\n",
    "            hist_exog = hist_exog.permute(0,2,1) # [B, C, L] -> [B, L, C]\n",
    "            insample_y = torch.cat(( insample_y, hist_exog.reshape(batch_size,-1) ), dim=1)\n",
    "\n",
    "        if self.futr_input_size > 0:\n",
    "            futr_exog = futr_exog.permute(0,2,1) # [B, L, C] -> [B, C, L]\n",
    "            futr_exog = self.pooling_layer(futr_exog)\n",
    "            futr_exog = futr_exog.permute(0,2,1) # [B, C, L] -> [B, L, C]\n",
    "            insample_y = torch.cat(( insample_y, futr_exog.reshape(batch_size,-1) ), dim=1)\n",
    "\n",
    "        if self.stat_input_size > 0:\n",
    "            insample_y = torch.cat(( insample_y, stat_exog.reshape(batch_size,-1) ), dim=1)\n",
    "\n",
    "        # Compute local projection weights and projection\n",
    "        theta = self.layers(insample_y)\n",
    "        backcast, forecast = self.basis(theta)\n",
    "        return backcast, forecast"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#| export\n",
    "class NHITS(BaseWindows):\n",
    "    \"\"\" NHITS\n",
    "\n",
    "    The Neural Hierarchical Interpolation for Time Series (NHITS), is an MLP-based deep\n",
    "    neural architecture with backward and forward residual links. NHITS tackles volatility and\n",
    "    memory complexity challenges, by locally specializing its sequential predictions into\n",
    "    the signals frequencies with hierarchical interpolation and pooling.\n",
    "\n",
    "    **Parameters:**<br>\n",
    "    `h`: int, Forecast horizon. <br>\n",
    "    `input_size`: int, autorregresive inputs size, y=[1,2,3,4] input_size=2 -> y_[t-2:t]=[1,2].<br>\n",
    "    `stat_exog_list`: str list, static exogenous columns.<br>\n",
    "    `hist_exog_list`: str list, historic exogenous columns.<br>\n",
    "    `futr_exog_list`: str list, future exogenous columns.<br>\n",
    "    `exclude_insample_y`: bool=False, the model skips the autoregressive features y[t-input_size:t] if True.<br>\n",
    "    `activation`: str, activation from ['ReLU', 'Softplus', 'Tanh', 'SELU', 'LeakyReLU', 'PReLU', 'Sigmoid'].<br>\n",
    "    `stack_types`: List[str], stacks list in the form N * ['identity'], to be deprecated in favor of `n_stacks`. Note that len(stack_types)=len(n_freq_downsample)=len(n_pool_kernel_size).<br>\n",
    "    `n_blocks`: List[int], Number of blocks for each stack. Note that len(n_blocks) = len(stack_types).<br>\n",
    "    `mlp_units`: List[List[int]], Structure of hidden layers for each stack type. Each internal list should contain the number of units of each hidden layer. Note that len(n_hidden) = len(stack_types).<br>\n",
    "    `n_freq_downsample`: List[int], list with the stack's coefficients (inverse expressivity ratios). Note that len(stack_types)=len(n_freq_downsample)=len(n_pool_kernel_size).<br>\n",
    "    `interpolation_mode`: str='linear', interpolation basis from ['linear', 'nearest', 'cubic'].<br>\n",
    "    `n_pool_kernel_size`: List[int], list with the size of the windows to take a max/avg over. Note that len(stack_types)=len(n_freq_downsample)=len(n_pool_kernel_size).<br>\n",
    "    `pooling_mode`: str, input pooling module from ['MaxPool1d', 'AvgPool1d'].<br>\n",
    "    `dropout_prob_theta`: float, Float between (0, 1). Dropout for NHITS basis.<br>\n",
    "    `loss`: PyTorch module, instantiated train loss class from [losses collection](https://nixtla.github.io/neuralforecast/losses.pytorch.html).<br>\n",
    "    `valid_loss`: PyTorch module=`loss`, instantiated valid loss class from [losses collection](https://nixtla.github.io/neuralforecast/losses.pytorch.html).<br>\n",
    "    `max_steps`: int=1000, maximum number of training steps.<br>\n",
    "    `learning_rate`: float=1e-3, Learning rate between (0, 1).<br>\n",
    "    `num_lr_decays`: int=-1, Number of learning rate decays, evenly distributed across max_steps.<br>\n",
    "    `early_stop_patience_steps`: int=-1, Number of validation iterations before early stopping.<br>\n",
    "    `val_check_steps`: int=100, Number of training steps between every validation loss check.<br>\n",
    "    `batch_size`: int=32, number of different series in each batch.<br>\n",
    "    `valid_batch_size`: int=None, number of different series in each validation and test batch, if None uses batch_size.<br>\n",
    "    `windows_batch_size`: int=1024, number of windows to sample in each training batch, default uses all.<br>\n",
    "    `inference_windows_batch_size`: int=-1, number of windows to sample in each inference batch, -1 uses all.<br>\n",
    "    `start_padding_enabled`: bool=False, if True, the model will pad the time series with zeros at the beginning, by input size.<br>\n",
    "    `step_size`: int=1, step size between each window of temporal data.<br>\n",
    "    `scaler_type`: str='identity', type of scaler for temporal inputs normalization see [temporal scalers](https://nixtla.github.io/neuralforecast/common.scalers.html).<br>\n",
    "    `random_seed`: int, random_seed for pytorch initializer and numpy generators.<br>\n",
    "    `num_workers_loader`: int=os.cpu_count(), workers to be used by `TimeSeriesDataLoader`.<br>\n",
    "    `drop_last_loader`: bool=False, if True `TimeSeriesDataLoader` drops last non-full batch.<br>\n",
    "    `alias`: str, optional,  Custom name of the model.<br>\n",
    "    `optimizer`: Subclass of 'torch.optim.Optimizer', optional, user specified optimizer instead of the default choice (Adam).<br>\n",
    "    `optimizer_kwargs`: dict, optional, list of parameters used by the user specified `optimizer`.<br>\n",
    "    `lr_scheduler`: Subclass of 'torch.optim.lr_scheduler.LRScheduler', optional, user specified lr_scheduler instead of the default choice (StepLR).<br>\n",
    "    `lr_scheduler_kwargs`: dict, optional, list of parameters used by the user specified `lr_scheduler`.<br>    \n",
    "    `**trainer_kwargs`: int,  keyword trainer arguments inherited from [PyTorch Lighning's trainer](https://pytorch-lightning.readthedocs.io/en/stable/api/pytorch_lightning.trainer.trainer.Trainer.html?highlight=trainer).<br>    \n",
    "\n",
    "    **References:**<br>\n",
    "    -[Cristian Challu, Kin G. Olivares, Boris N. Oreshkin, Federico Garza, \n",
    "    Max Mergenthaler-Canseco, Artur Dubrawski (2023). \"NHITS: Neural Hierarchical Interpolation for Time Series Forecasting\".\n",
    "    Accepted at the Thirty-Seventh AAAI Conference on Artificial Intelligence.](https://arxiv.org/abs/2201.12886)\n",
    "    \"\"\"\n",
    "    # Class attributes\n",
    "    SAMPLING_TYPE = 'windows'\n",
    "    EXOGENOUS_FUTR = True\n",
    "    EXOGENOUS_HIST = True\n",
    "    EXOGENOUS_STAT = True\n",
    "\n",
    "    def __init__(self, \n",
    "                 h,\n",
    "                 input_size,\n",
    "                 futr_exog_list = None,\n",
    "                 hist_exog_list = None,\n",
    "                 stat_exog_list = None,\n",
    "                 exclude_insample_y = False,\n",
    "                 stack_types: list = ['identity', 'identity', 'identity'],\n",
    "                 n_blocks: list = [1, 1, 1],\n",
    "                 mlp_units: list = 3 * [[512, 512]],\n",
    "                 n_pool_kernel_size: list = [2, 2, 1],\n",
    "                 n_freq_downsample: list = [4, 2, 1],\n",
    "                 pooling_mode: str = 'MaxPool1d',\n",
    "                 interpolation_mode: str = 'linear',\n",
    "                 dropout_prob_theta = 0.,\n",
    "                 activation = 'ReLU',\n",
    "                 loss = MAE(),\n",
    "                 valid_loss = None,\n",
    "                 max_steps: int = 1000,\n",
    "                 learning_rate: float = 1e-3,\n",
    "                 num_lr_decays: int = 3,\n",
    "                 early_stop_patience_steps: int =-1,\n",
    "                 val_check_steps: int = 100,\n",
    "                 batch_size: int = 32,\n",
    "                 valid_batch_size: Optional[int] = None,\n",
    "                 windows_batch_size: int = 1024,\n",
    "                 inference_windows_batch_size: int = -1,\n",
    "                 start_padding_enabled = False,\n",
    "                 step_size: int = 1,\n",
    "                 scaler_type: str = 'identity',\n",
    "                 random_seed: int = 1,\n",
    "                 num_workers_loader = 0,\n",
    "                 drop_last_loader = False,\n",
    "                 optimizer = None,\n",
    "                 optimizer_kwargs = None,\n",
    "                 lr_scheduler = None,\n",
    "                 lr_scheduler_kwargs = None,\n",
    "                 **trainer_kwargs):\n",
    "\n",
    "        # Inherit BaseWindows class\n",
    "        super(NHITS, self).__init__(h=h,\n",
    "                                    input_size=input_size,\n",
    "                                    futr_exog_list=futr_exog_list,\n",
    "                                    hist_exog_list=hist_exog_list,\n",
    "                                    stat_exog_list=stat_exog_list,\n",
    "                                    exclude_insample_y = exclude_insample_y,\n",
    "                                    loss=loss,\n",
    "                                    valid_loss=valid_loss,\n",
    "                                    max_steps=max_steps,\n",
    "                                    learning_rate=learning_rate,\n",
    "                                    num_lr_decays=num_lr_decays,\n",
    "                                    early_stop_patience_steps=early_stop_patience_steps,\n",
    "                                    val_check_steps=val_check_steps,\n",
    "                                    batch_size=batch_size,\n",
    "                                    windows_batch_size=windows_batch_size,\n",
    "                                    valid_batch_size=valid_batch_size,\n",
    "                                    inference_windows_batch_size=inference_windows_batch_size,\n",
    "                                    start_padding_enabled=start_padding_enabled,\n",
    "                                    step_size=step_size,\n",
    "                                    scaler_type=scaler_type,\n",
    "                                    num_workers_loader=num_workers_loader,\n",
    "                                    drop_last_loader=drop_last_loader,\n",
    "                                    random_seed=random_seed,\n",
    "                                    optimizer=optimizer,\n",
    "                                    optimizer_kwargs=optimizer_kwargs,\n",
    "                                    lr_scheduler=lr_scheduler,\n",
    "                                    lr_scheduler_kwargs=lr_scheduler_kwargs,\n",
    "                                    **trainer_kwargs)\n",
    "\n",
    "        # Architecture\n",
    "        blocks = self.create_stack(h=h,\n",
    "                                   input_size=input_size,\n",
    "                                   stack_types=stack_types,\n",
    "                                   futr_input_size=self.futr_exog_size,\n",
    "                                   hist_input_size=self.hist_exog_size,\n",
    "                                   stat_input_size=self.stat_exog_size,                                   \n",
    "                                   n_blocks=n_blocks,\n",
    "                                   mlp_units=mlp_units,\n",
    "                                   n_pool_kernel_size=n_pool_kernel_size,\n",
    "                                   n_freq_downsample=n_freq_downsample,\n",
    "                                   pooling_mode=pooling_mode,\n",
    "                                   interpolation_mode=interpolation_mode,\n",
    "                                   dropout_prob_theta=dropout_prob_theta,\n",
    "                                   activation=activation)\n",
    "        self.blocks = torch.nn.ModuleList(blocks)\n",
    "\n",
    "    def create_stack(self,\n",
    "                     h, \n",
    "                     input_size,    \n",
    "                     stack_types, \n",
    "                     n_blocks,\n",
    "                     mlp_units,\n",
    "                     n_pool_kernel_size,\n",
    "                     n_freq_downsample,\n",
    "                     pooling_mode,\n",
    "                     interpolation_mode,\n",
    "                     dropout_prob_theta, \n",
    "                     activation,\n",
    "                     futr_input_size, hist_input_size, stat_input_size):                     \n",
    "\n",
    "        block_list = []\n",
    "        for i in range(len(stack_types)):\n",
    "            for block_id in range(n_blocks[i]):\n",
    "\n",
    "                assert stack_types[i] == 'identity', f'Block type {stack_types[i]} not found!'\n",
    "\n",
    "                n_theta = (input_size + self.loss.outputsize_multiplier*max(h//n_freq_downsample[i], 1) )\n",
    "                basis = _IdentityBasis(backcast_size=input_size, forecast_size=h,\n",
    "                                       out_features=self.loss.outputsize_multiplier,\n",
    "                                       interpolation_mode=interpolation_mode)\n",
    "\n",
    "                nbeats_block = NHITSBlock(h=h,\n",
    "                                          input_size=input_size,\n",
    "                                          futr_input_size=futr_input_size,\n",
    "                                          hist_input_size=hist_input_size,\n",
    "                                          stat_input_size=stat_input_size,                                          \n",
    "                                          n_theta=n_theta,\n",
    "                                          mlp_units=mlp_units,\n",
    "                                          n_pool_kernel_size=n_pool_kernel_size[i],\n",
    "                                          pooling_mode=pooling_mode,\n",
    "                                          basis=basis,\n",
    "                                          dropout_prob=dropout_prob_theta,\n",
    "                                          activation=activation)\n",
    "\n",
    "                # Select type of evaluation and apply it to all layers of block\n",
    "                block_list.append(nbeats_block)\n",
    "                \n",
    "        return block_list\n",
    "\n",
    "    def forward(self, windows_batch):\n",
    "        \n",
    "        # Parse windows_batch\n",
    "        insample_y    = windows_batch['insample_y']\n",
    "        insample_mask = windows_batch['insample_mask']\n",
    "        futr_exog     = windows_batch['futr_exog']\n",
    "        hist_exog     = windows_batch['hist_exog']\n",
    "        stat_exog     = windows_batch['stat_exog']\n",
    "        \n",
    "        # insample\n",
    "        residuals = insample_y.flip(dims=(-1,)) #backcast init\n",
    "        insample_mask = insample_mask.flip(dims=(-1,))\n",
    "        \n",
    "        forecast = insample_y[:, -1:, None] # Level with Naive1\n",
    "        block_forecasts = [ forecast.repeat(1, self.h, 1) ]\n",
    "        for i, block in enumerate(self.blocks):\n",
    "            backcast, block_forecast = block(insample_y=residuals, futr_exog=futr_exog,\n",
    "                                             hist_exog=hist_exog, stat_exog=stat_exog)\n",
    "            residuals = (residuals - backcast) * insample_mask\n",
    "            forecast = forecast + block_forecast\n",
    "            \n",
    "            if self.decompose_forecast:\n",
    "                block_forecasts.append(block_forecast)\n",
    "        \n",
    "        # Adapting output's domain\n",
    "        forecast = self.loss.domain_map(forecast)\n",
    "\n",
    "        if self.decompose_forecast:\n",
    "            # (n_batch, n_blocks, h, output_size)\n",
    "            block_forecasts = torch.stack(block_forecasts)\n",
    "            block_forecasts = block_forecasts.permute(1,0,2,3)\n",
    "            block_forecasts = block_forecasts.squeeze(-1) # univariate output\n",
    "            return block_forecasts\n",
    "        else:\n",
    "            return forecast"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "show_doc(NHITS)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "show_doc(NHITS.fit, name='NHITS.fit')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "show_doc(NHITS.predict, name='NHITS.predict')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#| hide\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "import pytorch_lightning as pl\n",
    "\n",
    "from neuralforecast.utils import AirPassengersDF as Y_df\n",
    "from neuralforecast.tsdataset import TimeSeriesDataset, TimeSeriesLoader"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#| hide\n",
    "Y_train_df = Y_df[Y_df.ds<Y_df['ds'].values[-24]] # 132 train\n",
    "Y_test_df = Y_df[Y_df.ds>=Y_df['ds'].values[-24]] # 12 test\n",
    "\n",
    "dataset, *_ = TimeSeriesDataset.from_df(df = Y_train_df)\n",
    "model = NHITS(h=24,\n",
    "              input_size=24*2,\n",
    "              max_steps=1,\n",
    "              windows_batch_size=None, \n",
    "              n_freq_downsample=[12,4,1], \n",
    "              pooling_mode='MaxPool1d')\n",
    "model.fit(dataset=dataset)\n",
    "y_hat = model.predict(dataset=dataset)\n",
    "Y_test_df['NHITS'] = y_hat\n",
    "\n",
    "pd.concat([Y_train_df, Y_test_df]).drop('unique_id', axis=1).set_index('ds').plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#| hide\n",
    "# qualitative decomposition evaluation\n",
    "y_hat = model.decompose(dataset=dataset)\n",
    "\n",
    "fig, ax = plt.subplots(5, 1, figsize=(10, 15))\n",
    "\n",
    "ax[0].plot(Y_test_df['y'].values, label='True', color=\"#9C9DB2\", linewidth=4)\n",
    "ax[0].plot(y_hat.sum(axis=1).flatten(), label='Forecast', color=\"#7B3841\")\n",
    "ax[0].legend(prop={'size': 20})\n",
    "for label in (ax[0].get_xticklabels() + ax[0].get_yticklabels()):\n",
    "    label.set_fontsize(18)\n",
    "ax[0].set_ylabel('y', fontsize=20)\n",
    "\n",
    "ax[1].plot(y_hat[0,0], label='level', color=\"#7B3841\")\n",
    "ax[1].set_ylabel('Level', fontsize=20)\n",
    "\n",
    "ax[2].plot(y_hat[0,1], label='stack1', color=\"#7B3841\")\n",
    "ax[2].set_ylabel('Stack 1', fontsize=20)\n",
    "\n",
    "ax[3].plot(y_hat[0,2], label='stack2', color=\"#D9AE9E\")\n",
    "ax[3].set_ylabel('Stack 2', fontsize=20)\n",
    "\n",
    "ax[4].plot(y_hat[0,3], label='stack3', color=\"#D9AE9E\")\n",
    "ax[4].set_ylabel('Stack 3', fontsize=20)\n",
    "\n",
    "ax[4].set_xlabel('Prediction \\u03C4 \\u2208 {t+1,..., t+H}', fontsize=20)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Usage Example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#| eval: false\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import pytorch_lightning as pl\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from neuralforecast import NeuralForecast\n",
    "from neuralforecast.models import NHITS\n",
    "from neuralforecast.losses.pytorch import MQLoss, DistributionLoss, PMM, GMM, NBMM\n",
    "from neuralforecast.tsdataset import TimeSeriesDataset\n",
    "from neuralforecast.utils import AirPassengers, AirPassengersPanel, AirPassengersStatic\n",
    "\n",
    "\n",
    "Y_train_df = AirPassengersPanel[AirPassengersPanel.ds<AirPassengersPanel['ds'].values[-12]].reset_index(drop=True) # 132 train\n",
    "Y_test_df = AirPassengersPanel[AirPassengersPanel.ds>=AirPassengersPanel['ds'].values[-12]].reset_index(drop=True) # 12 test\n",
    "\n",
    "model = NHITS(h=12,\n",
    "              input_size=24,\n",
    "              loss=DistributionLoss(distribution='StudentT', level=[80, 90], return_params=True),\n",
    "              #loss=DistributionLoss(distribution='Normal', level=[80, 90], return_params=True),\n",
    "              #loss=DistributionLoss(distribution='Poisson', level=[80, 90], return_params=True),\n",
    "              #loss=DistributionLoss(distribution='Tweedie', level=[80, 90], rho=1.5),\n",
    "              #loss=DistributionLoss(distribution='NegativeBinomial', level=[80, 90], return_params=True),\n",
    "              #loss=NBMM(n_components=2, level=[80,90]),\n",
    "              #loss=GMM(n_components=2, level=[80,90]),\n",
    "              #loss=PMM(n_components=1, level=[80,90]),\n",
    "              stat_exog_list=['airline1'],\n",
    "              futr_exog_list=['trend'],\n",
    "              n_freq_downsample=[2, 1, 1],\n",
    "              scaler_type='robust',\n",
    "              max_steps=200,\n",
    "              early_stop_patience_steps=2,\n",
    "              inference_windows_batch_size=1,\n",
    "              val_check_steps=10,\n",
    "              learning_rate=1e-3)\n",
    "\n",
    "fcst = NeuralForecast(models=[model], freq='M')\n",
    "fcst.fit(df=Y_train_df, static_df=AirPassengersStatic, val_size=12)\n",
    "forecasts = fcst.predict(futr_df=Y_test_df)\n",
    "\n",
    "# Plot quantile predictions\n",
    "Y_hat_df = forecasts.reset_index(drop=False).drop(columns=['unique_id','ds'])\n",
    "plot_df = pd.concat([Y_test_df, Y_hat_df], axis=1)\n",
    "plot_df = pd.concat([Y_train_df, plot_df])\n",
    "\n",
    "plot_df = plot_df[plot_df.unique_id=='Airline1'].drop('unique_id', axis=1)\n",
    "plt.plot(plot_df['ds'], plot_df['y'], c='black', label='True')\n",
    "plt.plot(plot_df['ds'], plot_df['NHITS-median'], c='blue', label='median')\n",
    "plt.fill_between(x=plot_df['ds'][-12:], \n",
    "                 y1=plot_df['NHITS-lo-90'][-12:].values, \n",
    "                 y2=plot_df['NHITS-hi-90'][-12:].values,\n",
    "                 alpha=0.4, label='level 90')\n",
    "plt.legend()\n",
    "plt.grid()\n",
    "plt.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#| eval: false\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import pytorch_lightning as pl\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from neuralforecast import NeuralForecast\n",
    "from neuralforecast.models import NHITS\n",
    "from neuralforecast.losses.pytorch import DistributionLoss, HuberLoss, MAE\n",
    "from neuralforecast.tsdataset import TimeSeriesDataset\n",
    "from neuralforecast.utils import AirPassengers, AirPassengersPanel, AirPassengersStatic\n",
    "\n",
    "#AirPassengersPanel['y'] = 1 * (AirPassengersPanel['trend'] % 12) < 2\n",
    "Y_train_df = AirPassengersPanel[AirPassengersPanel.ds<AirPassengersPanel['ds'].values[-12]].reset_index(drop=True) # 132 train\n",
    "Y_test_df = AirPassengersPanel[AirPassengersPanel.ds>=AirPassengersPanel['ds'].values[-12]].reset_index(drop=True) # 12 test\n",
    "\n",
    "model = NHITS(h=12,\n",
    "              input_size=24,\n",
    "              #loss=DistributionLoss(distribution='StudentT', level=[80, 90], return_params=True),\n",
    "              loss=HuberLoss(delta=0.5),\n",
    "              valid_loss=MAE(),\n",
    "              stat_exog_list=['airline1'],\n",
    "              scaler_type='robust',\n",
    "              max_steps=200,\n",
    "              early_stop_patience_steps=2,\n",
    "              val_check_steps=10,\n",
    "              learning_rate=1e-3)\n",
    "\n",
    "fcst = NeuralForecast(models=[model], freq='M')\n",
    "fcst.fit(df=Y_train_df, static_df=AirPassengersStatic, val_size=12)\n",
    "forecasts = fcst.predict(futr_df=Y_test_df)\n",
    "\n",
    "# Plot quantile predictions\n",
    "Y_hat_df = forecasts.reset_index(drop=False).drop(columns=['unique_id','ds'])\n",
    "plot_df = pd.concat([Y_test_df, Y_hat_df], axis=1)\n",
    "plot_df = pd.concat([Y_train_df, plot_df])\n",
    "\n",
    "plot_df = plot_df[plot_df.unique_id=='Airline1'].drop('unique_id', axis=1)\n",
    "plt.plot(plot_df['ds'], plot_df['y'], c='black', label='True')\n",
    "plt.plot(plot_df['ds'], plot_df['NHITS'], c='blue', label='median')\n",
    "# plt.plot(plot_df['ds'], plot_df['NHITS-median'], c='blue', label='median')\n",
    "# plt.fill_between(x=plot_df['ds'][-12:], \n",
    "#                  y1=plot_df['NHITS-lo-90'][-12:].values, \n",
    "#                  y2=plot_df['NHITS-hi-90'][-12:].values,\n",
    "#                  alpha=0.4, label='level 90')\n",
    "plt.legend()\n",
    "plt.grid()\n",
    "plt.plot()"
   ]
  }
 ],
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